{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 04 - The Unreasonable Effectiveness of Linear Regression\n",
    " \n",
    " \n",
    "## All You Need is Linear Regression\n",
    " \n",
    " \n",
    "### Why We Need Models\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:47.845199Z",
     "start_time": "2023-06-25T15:09:45.813625Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import graphviz as gr\n",
    "from matplotlib import style\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "style.use(\"ggplot\")\n",
    "import statsmodels.formula.api as smf\n",
    "import matplotlib\n",
    "from cycler import cycler\n",
    "\n",
    "default_cycler = (cycler(color=['0.3', '0.5', '0.7', '0.5']))\n",
    "\n",
    "color=['0.3', '0.5', '0.7', '0.9']\n",
    "linestyle=['-', '--', ':', '-.']\n",
    "marker=['o', 'v', 'd', 'p']\n",
    "\n",
    "plt.rc('axes', prop_cycle=default_cycler)\n",
    "\n",
    "gr.set_default_format(\"png\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:48.081517Z",
     "start_time": "2023-06-25T15:09:47.854728Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
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       "<title>Risk&#45;&gt;X</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"79.92,-21.5 89.92,-18 79.92,-14.5 79.92,-21.5\"/>\n",
       "</g>\n",
       "<!-- Credit Limit -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>Credit Limit</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"235.25\" cy=\"-41\" rx=\"55.49\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"235.25\" y=\"-37.3\" font-family=\"Times,serif\" font-size=\"14.00\">Credit Limit</text>\n",
       "</g>\n",
       "<!-- X&#45;&gt;Credit Limit -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>X&#45;&gt;Credit Limit</title>\n",
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       "<title>Default</title>\n",
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       "<text text-anchor=\"middle\" x=\"363.54\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Default</text>\n",
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       "<!-- X&#45;&gt;Default -->\n",
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       "<title>X&#45;&gt;Default</title>\n",
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       "<title>Credit Limit&#45;&gt;Default</title>\n",
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x7f96e3826490>"
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     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_risk = gr.Digraph(graph_attr={\"rankdir\":\"LR\"})\n",
    "\n",
    "g_risk.edge(\"Risk\", \"X\")\n",
    "g_risk.edge(\"X\", \"Credit Limit\")\n",
    "g_risk.edge(\"X\", \"Default\")\n",
    "g_risk.edge(\"Credit Limit\", \"Default\")\n",
    "\n",
    "g_risk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression in A/B Tests\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:48.104171Z",
     "start_time": "2023-06-25T15:09:48.090446Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>recommender</th>\n",
       "      <th>age</th>\n",
       "      <th>tenure</th>\n",
       "      <th>watch_time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>challenger</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>2.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>challenger</td>\n",
       "      <td>27</td>\n",
       "      <td>1</td>\n",
       "      <td>2.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>benchmark</td>\n",
       "      <td>17</td>\n",
       "      <td>0</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>benchmark</td>\n",
       "      <td>34</td>\n",
       "      <td>1</td>\n",
       "      <td>1.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>benchmark</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>2.47</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  recommender  age  tenure  watch_time\n",
       "0  challenger   15       1        2.39\n",
       "1  challenger   27       1        2.32\n",
       "2   benchmark   17       0        2.74\n",
       "3   benchmark   34       1        1.92\n",
       "4   benchmark   14       1        2.47"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "data = pd.read_csv(\"./data/rec_ab_test.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:48.135005Z",
     "start_time": "2023-06-25T15:09:48.120084Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                <td></td>                  <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                    <td>    2.0491</td> <td>    0.058</td> <td>   35.367</td> <td> 0.000</td> <td>    1.935</td> <td>    2.163</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(recommender)[T.challenger]</th> <td>    0.1427</td> <td>    0.095</td> <td>    1.501</td> <td> 0.134</td> <td>   -0.044</td> <td>    0.330</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "\n",
    "result = smf.ols('watch_time ~ C(recommender)', data=data).fit()\n",
    "\n",
    "result.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:48.154510Z",
     "start_time": "2023-06-25T15:09:48.149312Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "recommender\n",
       "benchmark     2.049064\n",
       "challenger    2.191750\n",
       "Name: watch_time, dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(data\n",
    " .groupby(\"recommender\")\n",
    " [\"watch_time\"]\n",
    " .mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adjusting with Regression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:48.919026Z",
     "start_time": "2023-06-25T15:09:48.871583Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "\n",
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       "        vertical-align: top;\n",
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wage</th>\n",
       "      <th>educ</th>\n",
       "      <th>exper</th>\n",
       "      <th>married</th>\n",
       "      <th>credit_score1</th>\n",
       "      <th>credit_score2</th>\n",
       "      <th>credit_limit</th>\n",
       "      <th>default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>950.0</td>\n",
       "      <td>11</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>500.0</td>\n",
       "      <td>518.0</td>\n",
       "      <td>3200.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>780.0</td>\n",
       "      <td>11</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>414.0</td>\n",
       "      <td>429.0</td>\n",
       "      <td>1700.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1230.0</td>\n",
       "      <td>14</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>586.0</td>\n",
       "      <td>571.0</td>\n",
       "      <td>4200.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1040.0</td>\n",
       "      <td>15</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>379.0</td>\n",
       "      <td>411.0</td>\n",
       "      <td>1500.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1000.0</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>379.0</td>\n",
       "      <td>518.0</td>\n",
       "      <td>1800.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     wage  educ  exper  married  credit_score1  credit_score2  credit_limit  \\\n",
       "0   950.0    11     16        1          500.0          518.0        3200.0   \n",
       "1   780.0    11      7        1          414.0          429.0        1700.0   \n",
       "2  1230.0    14      9        1          586.0          571.0        4200.0   \n",
       "3  1040.0    15      8        1          379.0          411.0        1500.0   \n",
       "4  1000.0    16      1        1          379.0          518.0        1800.0   \n",
       "\n",
       "   default  \n",
       "0        0  \n",
       "1        0  \n",
       "2        0  \n",
       "3        0  \n",
       "4        0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "risk_data = pd.read_csv(\"./data/risk_data.csv\")\n",
    "\n",
    "risk_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:49.366423Z",
     "start_time": "2023-06-25T15:09:49.322580Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>    <td>    0.2192</td> <td>    0.004</td> <td>   59.715</td> <td> 0.000</td> <td>    0.212</td> <td>    0.226</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th> <td>-2.402e-05</td> <td> 1.16e-06</td> <td>  -20.689</td> <td> 0.000</td> <td>-2.63e-05</td> <td>-2.17e-05</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols('default ~ credit_limit', data=risk_data).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:09:50.530208Z",
     "start_time": "2023-06-25T15:09:50.301495Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Default Rate by Credit Limit')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (risk_data\n",
    "          .assign(size=1)\n",
    "          .groupby(\"credit_limit\")\n",
    "          .agg({\"default\": \"mean\", \"size\":sum})\n",
    "          .reset_index()\n",
    "          .assign(prediction = lambda d: model.predict(d)))\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "\n",
    "sns.scatterplot(data=plt_df,\n",
    "                x=\"credit_limit\",\n",
    "                y=\"default\",\n",
    "                size=\"size\",\n",
    "                sizes=(1,100))\n",
    "\n",
    "plt.plot(plt_df[\"credit_limit\"], plt_df[\"prediction\"], color=\"C1\")\n",
    "plt.title(\"Default Rate by Credit Limit\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:10:01.007172Z",
     "start_time": "2023-06-25T15:10:00.986084Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "credit_score1  credit_score2\n",
       "34.0           339.0            1\n",
       "               500.0            1\n",
       "52.0           518.0            1\n",
       "69.0           214.0            1\n",
       "               357.0            1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "risk_data.groupby([\"credit_score1\", \"credit_score2\"]).size().head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-25T15:10:01.442912Z",
     "start_time": "2023-06-25T15:10:01.381953Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>     <td>    0.4037</td> <td>    0.009</td> <td>   46.939</td> <td> 0.000</td> <td>    0.387</td> <td>    0.421</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th>  <td> 3.063e-06</td> <td> 1.54e-06</td> <td>    1.987</td> <td> 0.047</td> <td> 4.16e-08</td> <td> 6.08e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>wage</th>          <td>-8.822e-05</td> <td> 6.07e-06</td> <td>  -14.541</td> <td> 0.000</td> <td>   -0.000</td> <td>-7.63e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_score1</th> <td>-4.175e-05</td> <td> 1.83e-05</td> <td>   -2.278</td> <td> 0.023</td> <td>-7.77e-05</td> <td>-5.82e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_score2</th> <td>   -0.0003</td> <td> 1.52e-05</td> <td>  -20.055</td> <td> 0.000</td> <td>   -0.000</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = 'default ~ credit_limit + wage+credit_score1+credit_score2'\n",
    "model = smf.ols(formula, data=risk_data).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression Theory\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:45.659057Z",
     "start_time": "2023-05-12T11:02:45.650525Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.06252773e-06, -8.82159125e-05, -4.17472814e-05, -3.03928359e-04,\n",
       "        4.03661277e-01])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_cols = [\"credit_limit\", \"wage\", \"credit_score1\", \"credit_score2\"]\n",
    "X = risk_data[X_cols].assign(intercep=1)\n",
    "y = risk_data[\"default\"]\n",
    "\n",
    "def regress(y, X): \n",
    "    return np.linalg.inv(X.T.dot(X)).dot(X.T.dot(y))\n",
    "\n",
    "beta = regress(y, X)\n",
    "beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    "### Single Variable Linear Regression\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multivariate Linear Regression\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frisch-Waugh-Lovell Theorem and Orthogonalization\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:45.707252Z",
     "start_time": "2023-05-12T11:02:45.660874Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>     <td>    0.4037</td> <td>    0.009</td> <td>   46.939</td> <td> 0.000</td> <td>    0.387</td> <td>    0.421</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th>  <td> 3.063e-06</td> <td> 1.54e-06</td> <td>    1.987</td> <td> 0.047</td> <td> 4.16e-08</td> <td> 6.08e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>wage</th>          <td>-8.822e-05</td> <td> 6.07e-06</td> <td>  -14.541</td> <td> 0.000</td> <td>   -0.000</td> <td>-7.63e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_score1</th> <td>-4.175e-05</td> <td> 1.83e-05</td> <td>   -2.278</td> <td> 0.023</td> <td>-7.77e-05</td> <td>-5.82e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_score2</th> <td>   -0.0003</td> <td> 1.52e-05</td> <td>  -20.055</td> <td> 0.000</td> <td>   -0.000</td> <td>   -0.000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = 'default ~ credit_limit + wage+credit_score1+credit_score2'\n",
    "model = smf.ols(formula, data=risk_data).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Debiasing Step\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:45.848780Z",
     "start_time": "2023-05-12T11:02:45.709053Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Default Rate by Credit Limit')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (risk_data\n",
    "          .assign(size=1)\n",
    "          .groupby(\"credit_limit\")\n",
    "          .agg({\"default\": \"mean\", \"size\":sum})\n",
    "          .reset_index())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.scatterplot(data=plt_df,\n",
    "                x=\"credit_limit\",\n",
    "                y=\"default\",\n",
    "                size=\"size\",\n",
    "                sizes=(1,100))\n",
    "\n",
    "\n",
    "plt.title(\"Default Rate by Credit Limit\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:45.889451Z",
     "start_time": "2023-05-12T11:02:45.854239Z"
    }
   },
   "outputs": [],
   "source": [
    "debiasing_model = smf.ols(\n",
    "    'credit_limit ~ wage + credit_score1  + credit_score2',\n",
    "    data=risk_data\n",
    ").fit()\n",
    "\n",
    "risk_data_deb = risk_data.assign(\n",
    "    # for visualization, avg(T) is added to the residuals\n",
    "    credit_limit_res=(debiasing_model.resid \n",
    "                      + risk_data[\"credit_limit\"].mean())\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:45.914990Z",
     "start_time": "2023-05-12T11:02:45.890837Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>        <td>    0.1421</td> <td>    0.005</td> <td>   30.001</td> <td> 0.000</td> <td>    0.133</td> <td>    0.151</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit_res</th> <td> 3.063e-06</td> <td> 1.56e-06</td> <td>    1.957</td> <td> 0.050</td> <td>-4.29e-09</td> <td> 6.13e-06</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_w_deb_data = smf.ols('default ~ credit_limit_res',\n",
    "                           data=risk_data_deb).fit()\n",
    "\n",
    "model_w_deb_data.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.056997Z",
     "start_time": "2023-05-12T11:02:45.916989Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Default Rate by Debiased Credit Limit')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (risk_data_deb\n",
    "          .assign(size=1)\n",
    "          .assign(credit_limit_res = lambda d: d[\"credit_limit_res\"].round(-2))\n",
    "          .groupby(\"credit_limit_res\")\n",
    "          .agg({\"default\": \"mean\", \"size\":sum})\n",
    "          .query(\"size>30\")\n",
    "          .reset_index())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.scatterplot(data=plt_df,\n",
    "                x=\"credit_limit_res\",\n",
    "                y=\"default\",\n",
    "                size=\"size\",\n",
    "                sizes=(1,100))\n",
    "\n",
    "plt.title(\"Default Rate by Debiased Credit Limit\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Denoising Step\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.096204Z",
     "start_time": "2023-05-12T11:02:46.058746Z"
    }
   },
   "outputs": [],
   "source": [
    "denoising_model = smf.ols(\n",
    "    'default ~ wage + credit_score1  + credit_score2',\n",
    "    data=risk_data_deb\n",
    ").fit()\n",
    "\n",
    "risk_data_denoise = risk_data_deb.assign(\n",
    "    default_res=denoising_model.resid + risk_data_deb[\"default\"].mean()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard Error of the Regression Estimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.158157Z",
     "start_time": "2023-05-12T11:02:46.097819Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE regression: 5.364242347548197e-06\n",
      "SE formula:    5.364242347548201e-06\n"
     ]
    }
   ],
   "source": [
    "model_se = smf.ols(\n",
    "    'default ~ wage + credit_score1  + credit_score2',\n",
    "    data=risk_data\n",
    ").fit()\n",
    "\n",
    "print(\"SE regression:\", model_se.bse[\"wage\"])\n",
    "\n",
    "\n",
    "model_wage_aux = smf.ols(\n",
    "    'wage ~ credit_score1 + credit_score2',\n",
    "    data=risk_data\n",
    ").fit()\n",
    "\n",
    "# subtract the degrees of freedom - 4 model parameters - from N.\n",
    "se_formula = (np.std(model_se.resid)\n",
    "              /(np.std(model_wage_aux.resid)*np.sqrt(len(risk_data)-4)))\n",
    "\n",
    "print(\"SE formula:   \", se_formula)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Final Outcome Model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.184760Z",
     "start_time": "2023-05-12T11:02:46.159719Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>        <td>    0.1421</td> <td>    0.005</td> <td>   30.458</td> <td> 0.000</td> <td>    0.133</td> <td>    0.151</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit_res</th> <td> 3.063e-06</td> <td> 1.54e-06</td> <td>    1.987</td> <td> 0.047</td> <td> 4.17e-08</td> <td> 6.08e-06</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_w_orthogonal = smf.ols('default_res ~ credit_limit_res',\n",
    "                             data=risk_data_denoise).fit()\n",
    "\n",
    "model_w_orthogonal.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.331214Z",
     "start_time": "2023-05-12T11:02:46.186387Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Denoised Default Rate by Debiased Credit Limit')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (risk_data_denoise\n",
    "          .assign(size=1)\n",
    "          .assign(credit_limit_res = lambda d: d[\"credit_limit_res\"].round(-2))\n",
    "          .groupby(\"credit_limit_res\")\n",
    "          .agg({\"default_res\": \"mean\", \"size\":sum})\n",
    "          .query(\"size>30\")\n",
    "          .reset_index()\n",
    "          .assign(prediction = lambda d: model_w_orthogonal.predict(d)))\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.scatterplot(data=plt_df,\n",
    "                x=\"credit_limit_res\",\n",
    "                y=\"default_res\",\n",
    "                size=\"size\",\n",
    "                sizes=(1,100))\n",
    "\n",
    "plt.plot(plt_df[\"credit_limit_res\"], plt_df[\"prediction\"], c=\"C1\")\n",
    "\n",
    "plt.title(\"Denoised Default Rate by Debiased Credit Limit\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FWL Summary\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression as an Outcome Model\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Positivity and Extrapolation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.671640Z",
     "start_time": "2023-05-12T11:02:46.333383Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Dataset 2')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "n = 1000\n",
    "x = np.random.normal(0, 1, n)\n",
    "t = np.random.normal(x, 0.2, n) > 0\n",
    "\n",
    "y0 = x \n",
    "y1 = 1 + x\n",
    "\n",
    "y = np.random.normal((1-t)*y0 + t*y1, 0.2)\n",
    "\n",
    "df_no_pos = pd.DataFrame(dict(x=x,t=t.astype(int),y=y))\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6), sharey=True)\n",
    "\n",
    "sns.scatterplot(data=df_no_pos, x=\"x\", y=\"y\", hue=\"t\", ax=ax1, label=\"treatment\")\n",
    "\n",
    "m0 = smf.ols(\"y~x\", data=df_no_pos.query(f\"t==0\")).fit()\n",
    "m1 = smf.ols(\"y~x\", data=df_no_pos.query(f\"t==1\")).fit()\n",
    "\n",
    "sns.lineplot(data=df_no_pos.assign(pred=m0.predict(df_no_pos)), x=\"x\", y=\"pred\", color=f\"C0\", ax=ax1)\n",
    "sns.lineplot(data=df_no_pos.assign(pred=m1.predict(df_no_pos)), x=\"x\", y=\"pred\", color=f\"C1\", ax=ax1);\n",
    "ax1.set_title(\"Dataset 1\")\n",
    "\n",
    "np.random.seed(1)\n",
    "\n",
    "n = 1000\n",
    "x = np.random.normal(0, 1, n)\n",
    "t = np.random.binomial(1, 0.5, size=n)\n",
    "\n",
    "y0 = x * (x<0) + (x>0)*0\n",
    "y1 = 1 + x\n",
    "\n",
    "y = np.random.normal((1-t)*y0 + t*y1, 0.2)\n",
    "\n",
    "df_pos = pd.DataFrame(dict(x=x,t=t.astype(int),y=y))\n",
    "\n",
    "sns.scatterplot(data=df_pos, x=\"x\", hue=\"t\", y=\"y\", ax=ax2, label=\"treatment\")\n",
    "\n",
    "sns.lineplot(data=df_no_pos.assign(pred=m0.predict(df_pos)), x=\"x\", y=\"pred\", color=f\"C0\", ax=ax2)\n",
    "sns.lineplot(data=df_no_pos.assign(pred=m1.predict(df_pos)), x=\"x\", y=\"pred\", color=f\"C1\", ax=ax2)\n",
    "ax2.set_title(\"Dataset 2\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-Linearities in Linear Regression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.700699Z",
     "start_time": "2023-05-12T11:02:46.672696Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wage</th>\n",
       "      <th>educ</th>\n",
       "      <th>exper</th>\n",
       "      <th>married</th>\n",
       "      <th>credit_score1</th>\n",
       "      <th>credit_score2</th>\n",
       "      <th>credit_limit</th>\n",
       "      <th>spend</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>950.0</td>\n",
       "      <td>11</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>500.0</td>\n",
       "      <td>518.0</td>\n",
       "      <td>3200.0</td>\n",
       "      <td>3848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>780.0</td>\n",
       "      <td>11</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>414.0</td>\n",
       "      <td>429.0</td>\n",
       "      <td>1700.0</td>\n",
       "      <td>3144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1230.0</td>\n",
       "      <td>14</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>586.0</td>\n",
       "      <td>571.0</td>\n",
       "      <td>4200.0</td>\n",
       "      <td>4486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1040.0</td>\n",
       "      <td>15</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>379.0</td>\n",
       "      <td>411.0</td>\n",
       "      <td>1500.0</td>\n",
       "      <td>3327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1000.0</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>379.0</td>\n",
       "      <td>518.0</td>\n",
       "      <td>1800.0</td>\n",
       "      <td>3508</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     wage  educ  exper  married  credit_score1  credit_score2  credit_limit  \\\n",
       "0   950.0    11     16        1          500.0          518.0        3200.0   \n",
       "1   780.0    11      7        1          414.0          429.0        1700.0   \n",
       "2  1230.0    14      9        1          586.0          571.0        4200.0   \n",
       "3  1040.0    15      8        1          379.0          411.0        1500.0   \n",
       "4  1000.0    16      1        1          379.0          518.0        1800.0   \n",
       "\n",
       "   spend  \n",
       "0   3848  \n",
       "1   3144  \n",
       "2   4486  \n",
       "3   3327  \n",
       "4   3508  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spend_data = pd.read_csv(\"./data/spend_data.csv\")\n",
    "\n",
    "spend_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:46.929708Z",
     "start_time": "2023-05-12T11:02:46.702166Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.50.0 (0)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"318pt\" height=\"67pt\"\n",
       " viewBox=\"0.00 0.00 317.88 67.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 63)\">\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-63 313.88,-63 313.88,4 -4,4\"/>\n",
       "<!-- Wage -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>Wage</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"31.2\" cy=\"-18\" rx=\"31.4\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"31.2\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Wage</text>\n",
       "</g>\n",
       "<!-- Credit Limit -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>Credit Limit</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"153.64\" cy=\"-41\" rx=\"55.49\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"153.64\" y=\"-37.3\" font-family=\"Times,serif\" font-size=\"14.00\">Credit Limit</text>\n",
       "</g>\n",
       "<!-- Wage&#45;&gt;Credit Limit -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>Wage&#45;&gt;Credit Limit</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M61.05,-23.51C71.49,-25.5 83.67,-27.83 95.68,-30.12\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"95.21,-33.6 105.69,-32.03 96.52,-26.72 95.21,-33.6\"/>\n",
       "</g>\n",
       "<!-- Spend -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>Spend</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"277.38\" cy=\"-18\" rx=\"32.49\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"277.38\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Spend</text>\n",
       "</g>\n",
       "<!-- Wage&#45;&gt;Spend -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>Wage&#45;&gt;Spend</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M62.17,-15.8C73.51,-15.08 86.54,-14.36 98.39,-14 147.48,-12.52 159.8,-12.55 208.88,-14 217.23,-14.25 226.14,-14.67 234.67,-15.14\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"234.62,-18.64 244.81,-15.74 235.03,-11.66 234.62,-18.64\"/>\n",
       "</g>\n",
       "<!-- Credit Limit&#45;&gt;Spend -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>Credit Limit&#45;&gt;Spend</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M201.71,-32.11C213.18,-29.94 225.35,-27.64 236.46,-25.54\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"237.13,-28.98 246.31,-23.68 235.83,-22.1 237.13,-28.98\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x7fc7600ee450>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_risk = gr.Digraph(graph_attr={\"rankdir\":\"LR\"})\n",
    "\n",
    "g_risk.edge(\"Wage\", \"Credit Limit\")\n",
    "g_risk.edge(\"Wage\", \"Spend\")\n",
    "g_risk.edge(\"Credit Limit\", \"Spend\")\n",
    "\n",
    "g_risk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.164910Z",
     "start_time": "2023-05-12T11:02:46.931465Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='credit_limit', ylabel='spend'>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (spend_data\n",
    "          .assign(wage_group = lambda d: pd.IntervalIndex(pd.qcut(d[\"wage\"], 5)).mid)\n",
    "          .groupby([\"wage_group\", \"credit_limit\"])\n",
    "          [[\"spend\"]]\n",
    "          .mean()\n",
    "          .reset_index())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.scatterplot(data=plt_df, \n",
    "                x=\"credit_limit\",\n",
    "                y=\"spend\",\n",
    "                hue=\"wage_group\",\n",
    "                palette=\"gray\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![img](./data/img/code-img/04-img8.png)\n",
    "\n",
    "Rather, the treatment response curve seems to have some sort of concavity to it: the higher the credit limit, the lower the slope of this curve. Or, in causal inference language, since slopes and causal effects are intimately related, you can also say that the effect of lines on spend diminishes as you increase lines: going from a line of 1000 to 2000 increases spend more than going from 2000 to 3000. \n",
    " \n",
    "### Linearizing the Treatment\n",
    " \n",
    "To deal with that, you first need to transform the treatment into something that does have a linear relationship with the outcome. For instance, you know that the relationship seems concave, so you can try to apply some concave function to lines. Some good candidates to try out are the Log function, the square root function or any function that takes credit lines to the power of a fraction. \n",
    " \n",
    "In this case, let's try the square root:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.389071Z",
     "start_time": "2023-05-12T11:02:47.166140Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='credit_limit_sqrt', ylabel='spend'>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (spend_data\n",
    "          # apply the sqrt function to the treatment\n",
    "          .assign(credit_limit_sqrt = np.sqrt(spend_data[\"credit_limit\"]))\n",
    "          # create 5 wage binds for better vizualization\n",
    "          .assign(wage_group = pd.IntervalIndex(pd.qcut(spend_data[\"wage\"], 5)).mid)\n",
    "          .groupby([\"wage_group\", \"credit_limit_sqrt\"])\n",
    "          [[\"spend\"]]\n",
    "          .mean()\n",
    "          .reset_index())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.scatterplot(data=plt_df, \n",
    "                x=\"credit_limit_sqrt\",\n",
    "                y=\"spend\",\n",
    "                palette=\"gray\",\n",
    "                hue=\"wage_group\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.415659Z",
     "start_time": "2023-05-12T11:02:47.390568Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>             <td>  493.0044</td> <td>    6.501</td> <td>   75.832</td> <td> 0.000</td> <td>  480.262</td> <td>  505.747</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>np.sqrt(credit_limit)</th> <td>   63.2525</td> <td>    0.122</td> <td>  519.268</td> <td> 0.000</td> <td>   63.014</td> <td>   63.491</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_spend = smf.ols(\n",
    "    'spend ~ np.sqrt(credit_limit)',data=spend_data\n",
    ").fit()\n",
    "\n",
    "model_spend.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.607362Z",
     "start_time": "2023-05-12T11:02:47.417283Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='credit_limit', ylabel='spend'>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (spend_data\n",
    "          .assign(wage_group = lambda d: pd.IntervalIndex(pd.qcut(d[\"wage\"], 5)).mid)\n",
    "          .groupby([\"wage_group\", \"credit_limit\"])\n",
    "          [[\"spend\"]]\n",
    "          .mean()\n",
    "          .reset_index()\n",
    "         )\n",
    "\n",
    "x = np.linspace(plt_df[\"credit_limit\"].min(), plt_df[\"credit_limit\"].max())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(x, model_spend.params[0] + model_spend.params[1]*np.sqrt(x), color=\"C1\", label=\"prediction\", lw=4)\n",
    "plt.legend()\n",
    "sns.scatterplot(data=plt_df, \n",
    "                x=\"credit_limit\",\n",
    "                y=\"spend\",\n",
    "                palette=\"gray\",\n",
    "                hue=\"wage_group\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.640660Z",
     "start_time": "2023-05-12T11:02:47.608683Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>             <td>  383.5002</td> <td>    2.746</td> <td>  139.662</td> <td> 0.000</td> <td>  378.118</td> <td>  388.882</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>np.sqrt(credit_limit)</th> <td>   43.8504</td> <td>    0.065</td> <td>  672.633</td> <td> 0.000</td> <td>   43.723</td> <td>   43.978</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>wage</th>                  <td>    1.0459</td> <td>    0.002</td> <td>  481.875</td> <td> 0.000</td> <td>    1.042</td> <td>    1.050</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_spend = smf.ols('spend ~ np.sqrt(credit_limit)+wage',\n",
    "                      data=spend_data).fit()\n",
    "\n",
    "model_spend.summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-Linear FWL and Debiasing\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.701043Z",
     "start_time": "2023-05-12T11:02:47.642293Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>               <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>             <td> 1493.6990</td> <td>    3.435</td> <td>  434.818</td> <td> 0.000</td> <td> 1486.966</td> <td> 1500.432</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit_sqrt_deb</th> <td>   43.8504</td> <td>    0.065</td> <td>  672.640</td> <td> 0.000</td> <td>   43.723</td> <td>   43.978</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "debias_spend_model = smf.ols(f'np.sqrt(credit_limit) ~ wage',\n",
    "                             data=spend_data).fit()\n",
    "denoise_spend_model = smf.ols(f'spend ~ wage', data=spend_data).fit()\n",
    "\n",
    "\n",
    "credit_limit_sqrt_deb = (debias_spend_model.resid \n",
    "                         + np.sqrt(spend_data[\"credit_limit\"]).mean())\n",
    "spend_den = denoise_spend_model.resid + spend_data[\"spend\"].mean()\n",
    "\n",
    "\n",
    "spend_data_deb = (spend_data\n",
    "                  .assign(credit_limit_sqrt_deb = credit_limit_sqrt_deb,\n",
    "                          spend_den = spend_den))\n",
    "\n",
    "final_model = smf.ols(f'spend_den ~ credit_limit_sqrt_deb',\n",
    "                      data=spend_data_deb).fit()\n",
    "\n",
    "final_model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.927359Z",
     "start_time": "2023-05-12T11:02:47.703091Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='credit_limit', ylabel='spend'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (spend_data\n",
    "          .assign(wage_group = lambda d: pd.IntervalIndex(pd.qcut(d[\"wage\"], 5)).mid)\n",
    "          .groupby([\"wage_group\", \"credit_limit\"])\n",
    "          [[\"spend\"]]\n",
    "          .mean()\n",
    "          .reset_index())\n",
    "\n",
    "x = np.linspace(plt_df[\"credit_limit\"].min(), plt_df[\"credit_limit\"].max())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(x, (final_model.params[0] \n",
    "             + final_model.params[1]*np.sqrt(x)),\n",
    "         color=\"C1\", label=\"prediction\", lw=4)\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "sns.scatterplot(data=plt_df, \n",
    "                x=\"credit_limit\",\n",
    "                y=\"spend\",\n",
    "                palette=\"gray\",\n",
    "                hue=\"wage_group\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression for Dummies\n",
    " \n",
    "### Conditionally Random Experiments\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:47.942790Z",
     "start_time": "2023-05-12T11:02:47.928761Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wage</th>\n",
       "      <th>educ</th>\n",
       "      <th>exper</th>\n",
       "      <th>married</th>\n",
       "      <th>credit_score1</th>\n",
       "      <th>credit_score2</th>\n",
       "      <th>credit_score1_buckets</th>\n",
       "      <th>credit_limit</th>\n",
       "      <th>default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>890.0</td>\n",
       "      <td>11</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>490.0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>400</td>\n",
       "      <td>5400.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>670.0</td>\n",
       "      <td>11</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>196.0</td>\n",
       "      <td>481.0</td>\n",
       "      <td>200</td>\n",
       "      <td>3800.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1220.0</td>\n",
       "      <td>14</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>392.0</td>\n",
       "      <td>611.0</td>\n",
       "      <td>400</td>\n",
       "      <td>5800.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1210.0</td>\n",
       "      <td>15</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>627.0</td>\n",
       "      <td>519.0</td>\n",
       "      <td>600</td>\n",
       "      <td>6500.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>900.0</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>275.0</td>\n",
       "      <td>519.0</td>\n",
       "      <td>200</td>\n",
       "      <td>2100.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     wage  educ  exper  married  credit_score1  credit_score2  \\\n",
       "0   890.0    11     16        1          490.0          500.0   \n",
       "1   670.0    11      7        1          196.0          481.0   \n",
       "2  1220.0    14      9        1          392.0          611.0   \n",
       "3  1210.0    15      8        1          627.0          519.0   \n",
       "4   900.0    16      1        1          275.0          519.0   \n",
       "\n",
       "   credit_score1_buckets  credit_limit  default  \n",
       "0                    400        5400.0        0  \n",
       "1                    200        3800.0        0  \n",
       "2                    400        5800.0        0  \n",
       "3                    600        6500.0        0  \n",
       "4                    200        2100.0        0  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "risk_data_rnd = pd.read_csv(\"./data/risk_data_rnd.csv\")\n",
    "risk_data_rnd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.330665Z",
     "start_time": "2023-05-12T11:02:47.944140Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Conditional random experiment')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,6))\n",
    "sns.histplot(data=risk_data_rnd,\n",
    "             x=\"credit_limit\",\n",
    "             hue=\"credit_score1_buckets\",\n",
    "             kde=True,\n",
    "             palette=\"gray\");\n",
    "plt.title(\"Conditional random experiment\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dummy Variables\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.342917Z",
     "start_time": "2023-05-12T11:02:48.331844Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>    <td>    0.1369</td> <td>    0.009</td> <td>   15.081</td> <td> 0.000</td> <td>    0.119</td> <td>    0.155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th> <td>-9.344e-06</td> <td> 1.85e-06</td> <td>   -5.048</td> <td> 0.000</td> <td> -1.3e-05</td> <td>-5.72e-06</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols(\"default ~ credit_limit\", data=risk_data_rnd).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.346791Z",
     "start_time": "2023-05-12T11:02:48.344650Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "pd.set_option('display.max_columns', 9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.358062Z",
     "start_time": "2023-05-12T11:02:48.348218Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wage</th>\n",
       "      <th>educ</th>\n",
       "      <th>exper</th>\n",
       "      <th>married</th>\n",
       "      <th>...</th>\n",
       "      <th>sb_400</th>\n",
       "      <th>sb_600</th>\n",
       "      <th>sb_800</th>\n",
       "      <th>sb_1000</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>890.0</td>\n",
       "      <td>11</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>670.0</td>\n",
       "      <td>11</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1220.0</td>\n",
       "      <td>14</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1210.0</td>\n",
       "      <td>15</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>900.0</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 14 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     wage  educ  exper  married  ...  sb_400  sb_600  sb_800  sb_1000\n",
       "0   890.0    11     16        1  ...       1       0       0        0\n",
       "1   670.0    11      7        1  ...       0       0       0        0\n",
       "2  1220.0    14      9        1  ...       1       0       0        0\n",
       "3  1210.0    15      8        1  ...       0       1       0        0\n",
       "4   900.0    16      1        1  ...       0       0       0        0\n",
       "\n",
       "[5 rows x 14 columns]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "risk_data_dummies = (risk_data_rnd\n",
    "                     .join(pd.get_dummies(risk_data_rnd[\"credit_score1_buckets\"],\n",
    "                                          prefix=\"sb\",\n",
    "                                          drop_first=True)))\n",
    "risk_data_dummies.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.381603Z",
     "start_time": "2023-05-12T11:02:48.359512Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>    <td>    0.2253</td> <td>    0.056</td> <td>    4.000</td> <td> 0.000</td> <td>    0.115</td> <td>    0.336</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th> <td> 4.652e-06</td> <td> 2.02e-06</td> <td>    2.305</td> <td> 0.021</td> <td> 6.97e-07</td> <td> 8.61e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sb_200</th>       <td>   -0.0559</td> <td>    0.057</td> <td>   -0.981</td> <td> 0.327</td> <td>   -0.168</td> <td>    0.056</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sb_400</th>       <td>   -0.1442</td> <td>    0.057</td> <td>   -2.538</td> <td> 0.011</td> <td>   -0.256</td> <td>   -0.033</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sb_600</th>       <td>   -0.2148</td> <td>    0.057</td> <td>   -3.756</td> <td> 0.000</td> <td>   -0.327</td> <td>   -0.103</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sb_800</th>       <td>   -0.2489</td> <td>    0.060</td> <td>   -4.181</td> <td> 0.000</td> <td>   -0.366</td> <td>   -0.132</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sb_1000</th>      <td>   -0.2541</td> <td>    0.094</td> <td>   -2.715</td> <td> 0.007</td> <td>   -0.438</td> <td>   -0.071</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols(\n",
    "    \"default ~ credit_limit + sb_200+sb_400+sb_600+sb_800+sb_1000\",\n",
    "    data=risk_data_dummies\n",
    ").fit()\n",
    "\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.430041Z",
     "start_time": "2023-05-12T11:02:48.383003Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                  <td></td>                    <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                        <td>    0.2253</td> <td>    0.056</td> <td>    4.000</td> <td> 0.000</td> <td>    0.115</td> <td>    0.336</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.200]</th>  <td>   -0.0559</td> <td>    0.057</td> <td>   -0.981</td> <td> 0.327</td> <td>   -0.168</td> <td>    0.056</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.400]</th>  <td>   -0.1442</td> <td>    0.057</td> <td>   -2.538</td> <td> 0.011</td> <td>   -0.256</td> <td>   -0.033</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.600]</th>  <td>   -0.2148</td> <td>    0.057</td> <td>   -3.756</td> <td> 0.000</td> <td>   -0.327</td> <td>   -0.103</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.800]</th>  <td>   -0.2489</td> <td>    0.060</td> <td>   -4.181</td> <td> 0.000</td> <td>   -0.366</td> <td>   -0.132</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.1000]</th> <td>   -0.2541</td> <td>    0.094</td> <td>   -2.715</td> <td> 0.007</td> <td>   -0.438</td> <td>   -0.071</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th>                     <td> 4.652e-06</td> <td> 2.02e-06</td> <td>    2.305</td> <td> 0.021</td> <td> 6.97e-07</td> <td> 8.61e-06</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols(\"default ~ credit_limit + C(credit_score1_buckets)\",\n",
    "                data=risk_data_rnd).fit()\n",
    "\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.554890Z",
     "start_time": "2023-05-12T11:02:48.431682Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc79c685610>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (risk_data_rnd\n",
    "          .assign(risk_prediction = model.fittedvalues)\n",
    "          .groupby([\"credit_limit\", \"credit_score1_buckets\"])\n",
    "          [\"risk_prediction\"]\n",
    "          .mean()\n",
    "          .reset_index())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.lineplot(data=plt_df,\n",
    "             x=\"credit_limit\", y=\"risk_prediction\", hue=\"credit_score1_buckets\", palette = 'gray');\n",
    "plt.title(\"Fitted values by group\")\n",
    "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Saturated Regression Model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.578768Z",
     "start_time": "2023-05-12T11:02:48.556705Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "credit_score1_buckets\n",
       "0      -0.000071\n",
       "200     0.000007\n",
       "400     0.000005\n",
       "600     0.000003\n",
       "800     0.000002\n",
       "1000    0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def regress(df, t, y):\n",
    "    return smf.ols(f\"{y}~{t}\", data=df).fit().params[t]\n",
    "\n",
    "effect_by_group = (risk_data_rnd\n",
    "                   .groupby(\"credit_score1_buckets\")\n",
    "                   .apply(regress, y=\"default\", t=\"credit_limit\"))\n",
    "effect_by_group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.584830Z",
     "start_time": "2023-05-12T11:02:48.580087Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.490445628748722e-06"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "group_size = risk_data_rnd.groupby(\"credit_score1_buckets\").size()\n",
    "ate = (effect_by_group * group_size).sum() / group_size.sum()\n",
    "ate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.696265Z",
     "start_time": "2023-05-12T11:02:48.641114Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                        <td></td>                           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                                     <td>    0.3137</td> <td>    0.077</td> <td>    4.086</td> <td> 0.000</td> <td>    0.163</td> <td>    0.464</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.200]</th>               <td>   -0.1521</td> <td>    0.079</td> <td>   -1.926</td> <td> 0.054</td> <td>   -0.307</td> <td>    0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.400]</th>               <td>   -0.2339</td> <td>    0.078</td> <td>   -3.005</td> <td> 0.003</td> <td>   -0.386</td> <td>   -0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.600]</th>               <td>   -0.2957</td> <td>    0.080</td> <td>   -3.690</td> <td> 0.000</td> <td>   -0.453</td> <td>   -0.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.800]</th>               <td>   -0.3227</td> <td>    0.111</td> <td>   -2.919</td> <td> 0.004</td> <td>   -0.539</td> <td>   -0.106</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.1000]</th>              <td>   -0.3137</td> <td>    0.428</td> <td>   -0.733</td> <td> 0.464</td> <td>   -1.153</td> <td>    0.525</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th>                                  <td>-7.072e-05</td> <td> 4.45e-05</td> <td>   -1.588</td> <td> 0.112</td> <td>   -0.000</td> <td> 1.66e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit:C(credit_score1_buckets)[T.200]</th>  <td> 7.769e-05</td> <td> 4.48e-05</td> <td>    1.734</td> <td> 0.083</td> <td>-1.01e-05</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit:C(credit_score1_buckets)[T.400]</th>  <td> 7.565e-05</td> <td> 4.46e-05</td> <td>    1.696</td> <td> 0.090</td> <td>-1.18e-05</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit:C(credit_score1_buckets)[T.600]</th>  <td> 7.398e-05</td> <td> 4.47e-05</td> <td>    1.655</td> <td> 0.098</td> <td>-1.37e-05</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit:C(credit_score1_buckets)[T.800]</th>  <td> 7.286e-05</td> <td> 4.65e-05</td> <td>    1.567</td> <td> 0.117</td> <td>-1.83e-05</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit:C(credit_score1_buckets)[T.1000]</th> <td> 7.072e-05</td> <td> 8.05e-05</td> <td>    0.878</td> <td> 0.380</td> <td>-8.71e-05</td> <td>    0.000</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols(\"default ~ credit_limit * C(credit_score1_buckets)\",\n",
    "                data=risk_data_rnd).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.702228Z",
     "start_time": "2023-05-12T11:02:48.697590Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "credit_limit:C(credit_score1_buckets)[T.200]     0.000007\n",
       "credit_limit:C(credit_score1_buckets)[T.400]     0.000005\n",
       "credit_limit:C(credit_score1_buckets)[T.600]     0.000003\n",
       "credit_limit:C(credit_score1_buckets)[T.800]     0.000002\n",
       "credit_limit:C(credit_score1_buckets)[T.1000]    0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(model.params[model.params.index.str.contains(\"credit_limit:\")]\n",
    " + model.params[\"credit_limit\"]).round(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.828411Z",
     "start_time": "2023-05-12T11:02:48.703481Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc78a026f50>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_df = (risk_data_rnd\n",
    "          .assign(risk_prediction = model.fittedvalues)\n",
    "          .groupby([\"credit_limit\", \"credit_score1_buckets\"])\n",
    "          [\"risk_prediction\"]\n",
    "          .mean()\n",
    "          .reset_index())\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "sns.lineplot(data=plt_df,\n",
    "             x=\"credit_limit\", y=\"risk_prediction\", hue=\"credit_score1_buckets\",  palette=\"gray\");\n",
    "plt.title(\"Fitted values by group\")\n",
    "plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression as Variance Weighted Average\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.837985Z",
     "start_time": "2023-05-12T11:02:48.830057Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t</th>\n",
       "      <th>y</th>\n",
       "      <th>g</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-1.085631</td>\n",
       "      <td>-1.085631</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.997345</td>\n",
       "      <td>0.997345</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.282978</td>\n",
       "      <td>0.282978</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.506295</td>\n",
       "      <td>-1.506295</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.578600</td>\n",
       "      <td>-0.578600</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          t         y  g\n",
       "0 -1.085631 -1.085631  1\n",
       "1  0.997345  0.997345  1\n",
       "2  0.282978  0.282978  1\n",
       "3 -1.506295 -1.506295  1\n",
       "4 -0.578600 -0.578600  1"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "\n",
    "# std(t)=1\n",
    "t1 = np.random.normal(0, 1, size=1000)\n",
    "df1 = pd.DataFrame(dict(\n",
    "    t=t1,\n",
    "    y=1*t1, # ATE of 1\n",
    "    g=1,\n",
    "))\n",
    "\n",
    "# std(t)=2\n",
    "t2 = np.random.normal(0, 2, size=500)\n",
    "df2 = pd.DataFrame(dict(\n",
    "    t=t2,\n",
    "    y=2*t2, # ATE of 2\n",
    "    g=2,\n",
    "))\n",
    "\n",
    "df = pd.concat([df1, df2])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.850911Z",
     "start_time": "2023-05-12T11:02:48.839720Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.333333333333333"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "effect_by_group = df.groupby(\"g\").apply(regress, y=\"y\", t=\"t\")\n",
    "ate = (effect_by_group *\n",
    "       df.groupby(\"g\").size()).sum() / df.groupby(\"g\").size().sum()\n",
    "ate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.865544Z",
     "start_time": "2023-05-12T11:02:48.852685Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    0.024758\n",
       "C(g)[T.2]    0.019860\n",
       "t            1.625775\n",
       "dtype: float64"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols(\"y ~ t + C(g)\", data=df).fit()\n",
    "model.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### De-Meaning and Fixed Effects\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.912734Z",
     "start_time": "2023-05-12T11:02:48.867121Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                  <td></td>                    <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                        <td> 1173.0769</td> <td>  278.994</td> <td>    4.205</td> <td> 0.000</td> <td>  626.193</td> <td> 1719.961</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.200]</th>  <td> 2195.4337</td> <td>  281.554</td> <td>    7.798</td> <td> 0.000</td> <td> 1643.530</td> <td> 2747.337</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.400]</th>  <td> 3402.3796</td> <td>  279.642</td> <td>   12.167</td> <td> 0.000</td> <td> 2854.224</td> <td> 3950.535</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.600]</th>  <td> 4191.3235</td> <td>  280.345</td> <td>   14.951</td> <td> 0.000</td> <td> 3641.790</td> <td> 4740.857</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.800]</th>  <td> 4639.5105</td> <td>  291.400</td> <td>   15.921</td> <td> 0.000</td> <td> 4068.309</td> <td> 5210.712</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.1000]</th> <td> 5006.9231</td> <td>  461.255</td> <td>   10.855</td> <td> 0.000</td> <td> 4102.771</td> <td> 5911.076</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_deb = smf.ols(\"credit_limit ~ C(credit_score1_buckets)\",\n",
    "                    data=risk_data_rnd).fit()\n",
    "model_deb.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.918850Z",
     "start_time": "2023-05-12T11:02:48.914449Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "credit_score1_buckets\n",
       "0       1173.076923\n",
       "200     3368.510638\n",
       "400     4575.456498\n",
       "600     5364.400448\n",
       "800     5812.587413\n",
       "1000    6180.000000\n",
       "Name: credit_limit, dtype: float64"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "risk_data_rnd.groupby(\"credit_score1_buckets\")[\"credit_limit\"].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.924170Z",
     "start_time": "2023-05-12T11:02:48.920104Z"
    }
   },
   "outputs": [],
   "source": [
    "risk_data_fe = risk_data_rnd.assign(\n",
    "    credit_limit_avg = lambda d: (d\n",
    "                                  .groupby(\"credit_score1_buckets\")\n",
    "                                  [\"credit_limit\"].transform(\"mean\"))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.938351Z",
     "start_time": "2023-05-12T11:02:48.925781Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                   <td></td>                     <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                          <td>    0.0935</td> <td>    0.003</td> <td>   32.121</td> <td> 0.000</td> <td>    0.088</td> <td>    0.099</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>I(credit_limit - credit_limit_avg)</th> <td> 4.652e-06</td> <td> 2.05e-06</td> <td>    2.273</td> <td> 0.023</td> <td>  6.4e-07</td> <td> 8.66e-06</td>\n",
       "</tr>\n",
       "</table>"
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      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
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     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols(\"default ~ I(credit_limit-credit_limit_avg)\",\n",
    "                data=risk_data_fe).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:48.954283Z",
     "start_time": "2023-05-12T11:02:48.939976Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>        <td>    0.4325</td> <td>    0.020</td> <td>   21.418</td> <td> 0.000</td> <td>    0.393</td> <td>    0.472</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th>     <td> 4.652e-06</td> <td> 2.02e-06</td> <td>    2.305</td> <td> 0.021</td> <td> 6.96e-07</td> <td> 8.61e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit_avg</th> <td>-7.763e-05</td> <td> 4.75e-06</td> <td>  -16.334</td> <td> 0.000</td> <td>-8.69e-05</td> <td>-6.83e-05</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.table.SimpleTable'>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = smf.ols(\"default ~ credit_limit + credit_limit_avg\",\n",
    "                data=risk_data_fe).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Omitted Variable Bias: Confounding Through the Lens of Regression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.131659Z",
     "start_time": "2023-05-12T11:02:48.955782Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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       "<text text-anchor=\"middle\" x=\"128.94\" y=\"-37.3\" font-family=\"Times,serif\" font-size=\"14.00\">Lines</text>\n",
       "</g>\n",
       "<!-- Default -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>Default</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"232.54\" cy=\"-18\" rx=\"37.09\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"232.54\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Default</text>\n",
       "</g>\n",
       "<!-- Lines&#45;&gt;Default -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>Lines&#45;&gt;Default</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M157.7,-34.72C167.32,-32.54 178.33,-30.04 188.87,-27.66\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"189.78,-31.04 198.76,-25.42 188.24,-24.21 189.78,-31.04\"/>\n",
       "</g>\n",
       "<!-- Wage -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>Wage</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"31.2\" cy=\"-18\" rx=\"31.4\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"31.2\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Wage</text>\n",
       "</g>\n",
       "<!-- Wage&#45;&gt;Lines -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>Wage&#45;&gt;Lines</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M60.15,-24.71C69.67,-27 80.47,-29.6 90.61,-32.03\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"89.91,-35.46 100.45,-34.4 91.55,-28.66 89.91,-35.46\"/>\n",
       "</g>\n",
       "<!-- Wage&#45;&gt;Default -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>Wage&#45;&gt;Default</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M62.17,-15.8C73.51,-15.08 86.54,-14.36 98.39,-14 125.54,-13.18 132.35,-13.25 159.49,-14 167.95,-14.23 176.96,-14.62 185.65,-15.07\"/>\n",
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       "<graphviz.graphs.Digraph at 0x7fc79caa6ad0>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = gr.Digraph(graph_attr={\"rankdir\":\"LR\"})\n",
    "\n",
    "\n",
    "g.edge(\"Lines\", \"Default\")\n",
    "g.edge(\"Wage\", \"Default\"),\n",
    "g.edge(\"Wage\", \"Lines\")\n",
    "\n",
    "\n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.158827Z",
     "start_time": "2023-05-12T11:02:49.133769Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.401961992596885e-05"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "short_model = smf.ols(\"default ~ credit_limit\", data=risk_data).fit()\n",
    "short_model.params[\"credit_limit\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.217992Z",
     "start_time": "2023-05-12T11:02:49.163681Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.4019619925968762e-05"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "long_model = smf.ols(\"default ~ credit_limit + wage\",\n",
    "                     data=risk_data).fit()\n",
    "\n",
    "omitted_model = smf.ols(\"wage ~ credit_limit\", data=risk_data).fit()\n",
    "\n",
    "(long_model.params[\"credit_limit\"] \n",
    " + long_model.params[\"wage\"]*omitted_model.params[\"credit_limit\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neutral Controls\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.384088Z",
     "start_time": "2023-05-12T11:02:49.219727Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
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       "<title>credit_score1_buckets</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"89.04\" cy=\"-95\" rx=\"89.08\" ry=\"18\"/>\n",
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       "<!-- Default -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>Default</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"402.82\" cy=\"-72\" rx=\"37.09\" ry=\"18\"/>\n",
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       "<!-- credit_score1_buckets&#45;&gt;Lines -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>credit_score1_buckets&#45;&gt;Lines</title>\n",
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       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>Lines&#45;&gt;Default</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"355.49,-75.5 365.49,-72 355.49,-68.5 355.49,-75.5\"/>\n",
       "</g>\n",
       "<!-- credit_score2 -->\n",
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       "<title>credit_score2</title>\n",
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       "</g>\n",
       "<!-- credit_score2&#45;&gt;Default -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>credit_score2&#45;&gt;Default</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M307.13,-32.33C324.75,-39.71 346.27,-48.73 364.34,-56.3\"/>\n",
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       "</g>\n",
       "</svg>\n"
      ],
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       "<graphviz.graphs.Digraph at 0x7fc79cab3590>"
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     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = gr.Digraph(graph_attr={\"rankdir\":\"LR\"})\n",
    "\n",
    "g.edge(\"credit_score1_buckets\", \"Default\"),\n",
    "g.edge(\"credit_score1_buckets\", \"Lines\"),\n",
    "g.edge(\"credit_score2\", \"Default\"),\n",
    "g.edge(\"Lines\", \"Default\")\n",
    "\n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.440161Z",
     "start_time": "2023-05-12T11:02:49.386357Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "                  <td></td>                    <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                        <td>    0.5576</td> <td>    0.055</td> <td>   10.132</td> <td> 0.000</td> <td>    0.450</td> <td>    0.665</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.200]</th>  <td>   -0.0387</td> <td>    0.055</td> <td>   -0.710</td> <td> 0.478</td> <td>   -0.146</td> <td>    0.068</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.400]</th>  <td>   -0.1032</td> <td>    0.054</td> <td>   -1.898</td> <td> 0.058</td> <td>   -0.210</td> <td>    0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.600]</th>  <td>   -0.1410</td> <td>    0.055</td> <td>   -2.574</td> <td> 0.010</td> <td>   -0.248</td> <td>   -0.034</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.800]</th>  <td>   -0.1161</td> <td>    0.057</td> <td>   -2.031</td> <td> 0.042</td> <td>   -0.228</td> <td>   -0.004</td>\n",
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       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.1000]</th> <td>   -0.0430</td> <td>    0.090</td> <td>   -0.479</td> <td> 0.632</td> <td>   -0.219</td> <td>    0.133</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_limit</th>                     <td> 4.928e-06</td> <td> 1.93e-06</td> <td>    2.551</td> <td> 0.011</td> <td> 1.14e-06</td> <td> 8.71e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>credit_score2</th>                    <td>   -0.0007</td> <td> 2.34e-05</td> <td>  -30.225</td> <td> 0.000</td> <td>   -0.001</td> <td>   -0.001</td>\n",
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     "execution_count": 56,
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   ],
   "source": [
    "formula = \"default~credit_limit+C(credit_score1_buckets)+credit_score2\"\n",
    "model = smf.ols(formula, data=risk_data_rnd).fit()\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Noise Inducing Control\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.600381Z",
     "start_time": "2023-05-12T11:02:49.442100Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
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       "<title>credit_score1_buckets&#45;&gt;Lines</title>\n",
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    "g = gr.Digraph(graph_attr={\"rankdir\":\"LR\"})\n",
    "\n",
    "\n",
    "g.edge(\"credit_score1_buckets\", \"Lines\"),\n",
    "g.edge(\"U\", \"Spend\"),\n",
    "g.edge(\"Lines\", \"Spend\")\n",
    "\n",
    "g"
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  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.615600Z",
     "start_time": "2023-05-12T11:02:49.602050Z"
    }
   },
   "outputs": [
    {
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       "  <th>np.sqrt(credit_limit)</th> <td>   16.2915</td> <td>    2.988</td> <td>    5.452</td> <td> 0.000</td> <td>   10.420</td> <td>   22.163</td>\n",
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    "spend_data_rnd = pd.read_csv(\"data/spend_data_rnd.csv\")\n",
    "\n",
    "model = smf.ols(\"spend ~ np.sqrt(credit_limit)\",\n",
    "                data=spend_data_rnd).fit()\n",
    "\n",
    "model.summary().tables[1]"
   ]
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   "execution_count": 59,
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     "start_time": "2023-05-12T11:02:49.617433Z"
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       "  <th>Intercept</th>                        <td> 2367.4867</td> <td>  556.273</td> <td>    4.256</td> <td> 0.000</td> <td> 1274.528</td> <td> 3460.446</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.200]</th>  <td> -144.7921</td> <td>  591.613</td> <td>   -0.245</td> <td> 0.807</td> <td>-1307.185</td> <td> 1017.601</td>\n",
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       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.400]</th>  <td> -118.3923</td> <td>  565.364</td> <td>   -0.209</td> <td> 0.834</td> <td>-1229.211</td> <td>  992.427</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(credit_score1_buckets)[T.600]</th>  <td> -111.5738</td> <td>  570.471</td> <td>   -0.196</td> <td> 0.845</td> <td>-1232.429</td> <td> 1009.281</td>\n",
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       "</tr>\n",
       "<tr>\n",
       "  <th>np.sqrt(credit_limit)</th>            <td>   14.5953</td> <td>    3.523</td> <td>    4.142</td> <td> 0.000</td> <td>    7.673</td> <td>   21.518</td>\n",
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   ],
   "source": [
    "model = smf.ols(\"spend~np.sqrt(credit_limit)+C(credit_score1_buckets)\",\n",
    "                data=spend_data_rnd).fit()\n",
    "\n",
    "model.summary().tables[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature Selection: A Bias-Variance Trade-Off\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.835553Z",
     "start_time": "2023-05-12T11:02:49.631596Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
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    "g = gr.Digraph(graph_attr={\"rankdir\": \"LR\"})\n",
    "\n",
    "\n",
    "g.edge(\"X1\", \"T\", penwidth=\"5\"),\n",
    "g.edge(\"X2\", \"T\", penwidth=\"3\"),\n",
    "g.edge(\"X3\", \"T\", penwidth=\"1\"),\n",
    "\n",
    "g.edge(\"X1\", \"Y\", penwidth=\"1\"),\n",
    "g.edge(\"X2\", \"Y\", penwidth=\"3\"),\n",
    "g.edge(\"X3\", \"Y\", penwidth=\"5\"),\n",
    "\n",
    "g.edge(\"T\", \"Y\"),\n",
    "\n",
    "g"
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  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:49.852980Z",
     "start_time": "2023-05-12T11:02:49.837739Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "  <th>x2</th>        <td>    0.0143</td> <td>    3.128</td> <td>    0.005</td> <td> 0.996</td> <td>   -6.195</td> <td>    6.224</td>\n",
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       "  <th>x3</th>        <td>    9.6292</td> <td>    0.887</td> <td>   10.861</td> <td> 0.000</td> <td>    7.869</td> <td>   11.389</td>\n",
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   "source": [
    "np.random.seed(123)\n",
    "\n",
    "n = 100\n",
    "(x1, x2, x3) = (np.random.normal(0, 1, n) for _ in range(3))\n",
    "t = np.random.normal(10*x1 + 5*x2 + x3)\n",
    "\n",
    "# ate = 0.05\n",
    "y = np.random.normal(0.05*t + x1 + 5*x2 + 10*x3, 5)\n",
    "df = pd.DataFrame(dict(y=y, t=t, x1=x1, x2=x2, x3=x3))\n",
    "\n",
    "smf.ols(\"y~t+x1+x2+x3\", data=df).fit().summary().tables[1]"
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   "cell_type": "code",
   "execution_count": 62,
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     "end_time": "2023-05-12T11:02:49.864735Z",
     "start_time": "2023-05-12T11:02:49.854195Z"
    }
   },
   "outputs": [
    {
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    "smf.ols(\"y~t+x2+x3\", data=df).fit().summary().tables[1]"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Key Ideas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-05-12T11:02:50.050118Z",
     "start_time": "2023-05-12T11:02:49.865957Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
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       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-184 391.59,-184 391.59,4 -4,4\"/>\n",
       "<!-- Parent&#39;s Income -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>Parent&#39;s Income</title>\n",
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       "<text text-anchor=\"middle\" x=\"67.59\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\">Parent&#39;s Income</text>\n",
       "</g>\n",
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       "<title>Private</title>\n",
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       "</g>\n",
       "<!-- Parent&#39;s Income&#45;&gt;Private -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>Parent&#39;s Income&#45;&gt;Private</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"186.33,-110.17 193.95,-102.81 183.4,-103.81 186.33,-110.17\"/>\n",
       "</g>\n",
       "<!-- Income -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>Income</title>\n",
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       "<text text-anchor=\"middle\" x=\"219.59\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Income</text>\n",
       "</g>\n",
       "<!-- Parent&#39;s Income&#45;&gt;Income -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>Parent&#39;s Income&#45;&gt;Income</title>\n",
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       "</g>\n",
       "<!-- Private&#45;&gt;Income -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>Private&#45;&gt;Income</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"223.09,-46.1 219.59,-36.1 216.09,-46.1 223.09,-46.1\"/>\n",
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       "<!-- SAT -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>SAT</title>\n",
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       "<text text-anchor=\"middle\" x=\"180.59\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\">SAT</text>\n",
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       "<!-- SAT&#45;&gt;Private -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>SAT&#45;&gt;Private</title>\n",
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       "<!-- SAT&#45;&gt;Income -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>SAT&#45;&gt;Income</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M175.43,-144.02C170.76,-125.66 165.84,-95.84 174.59,-72 178.74,-60.72 186.46,-50.2 194.35,-41.56\"/>\n",
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       "</g>\n",
       "<!-- Ambition -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>Ambition</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"270.59\" cy=\"-162\" rx=\"44.69\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"270.59\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\">Ambition</text>\n",
       "</g>\n",
       "<!-- Ambition&#45;&gt;Private -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>Ambition&#45;&gt;Private</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M258.51,-144.41C252.28,-135.87 244.57,-125.28 237.65,-115.79\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"240.31,-113.49 231.59,-107.47 234.65,-117.61 240.31,-113.49\"/>\n",
       "</g>\n",
       "<!-- Ambition&#45;&gt;Income -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>Ambition&#45;&gt;Income</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M272.53,-143.9C273.92,-125.44 274.15,-95.53 264.59,-72 260.07,-60.87 252.27,-50.38 244.41,-41.72\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"246.74,-39.09 237.28,-34.31 241.69,-43.94 246.74,-39.09\"/>\n",
       "</g>\n",
       "<!-- ... -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>...</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"360.59\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"360.59\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\">...</text>\n",
       "</g>\n",
       "<!-- ...&#45;&gt;Private -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>...&#45;&gt;Private</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M339.48,-150.52C316.67,-139.19 279.98,-120.98 253.2,-107.68\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"254.69,-104.51 244.17,-103.2 251.57,-110.78 254.69,-104.51\"/>\n",
       "</g>\n",
       "<!-- ...&#45;&gt;Income -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>...&#45;&gt;Income</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M348.32,-145.95C333.27,-127.78 306.66,-96.6 281.59,-72 270.45,-61.06 257.41,-49.72 246.17,-40.34\"/>\n",
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x7fc78a5479d0>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz as gr\n",
    "\n",
    "g = gr.Digraph(format=\"png\")\n",
    "\n",
    "g.edge(\"Parent's Income\", \"Private\")\n",
    "g.edge(\"SAT\", \"Private\")\n",
    "g.edge(\"Ambition\", \"Private\")\n",
    "g.edge(\"...\", \"Private\")\n",
    "\n",
    "g.edge(\"Parent's Income\", \"Income\")\n",
    "g.edge(\"SAT\", \"Income\")\n",
    "g.edge(\"Ambition\", \"Income\")\n",
    "g.edge(\"...\", \"Income\")\n",
    "\n",
    "g.edge(\"Private\", \"Income\")\n",
    "\n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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